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arXiv · 2010.15074

Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d $\mathcal{N} = 2$ theories

Shi Cheng
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Abstract

We study the mirror symmetry of abelian 3d $\mathcal{N}=2$ theories with mixed Chern-Simons levels by turning them into $\mathcal{T}_{A,N}$ theories that are defined as $N$ copies of $U(1)-[1]$ theory coupled together by mixed Chern-Simons levels $k_{ij}$. We find that $\mathcal{T}_{A,N}$ theories have many mirror dual theories with different mixed CS levels and FI parameters. As an example, we analyze $U(1)_k+ N_C \,\mathbf{C} + N_{AC} \, \mathbf{AC}$ theories by transforming these theories into certain $\mathcal{T}_{A,N}$ theories and find many equivalent effective Chern-Simons levels. Finally, we analyze mirror symmetry for theories corresponding to knots. In this work we use sphere partition functions and vortex partition functions to derive dual theories.

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Shi Cheng. 2020-10-28. Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d $\mathcal{N} = 2$ theories. https://doi.org/10.1103/physrevd.104.046011

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